Random Generation of Positive TAGEDs wrt. the Emptiness Problem

Tree automata are a widely used formalism in Computer Science. Since their creation in the fifties, numerous more expressive extensions have been proposed. Unfortunately, the decision problems associated with these extensions are quite often undecidable or in prohibitive classes of algorithmic complexity (NP-complete or worse), and little work has gone into finding efficient heuristics for them. Beyond the inherent difficulty of those problems, a common hitch in this line of research is the experimental evaluation of new algorithms. As those extensions of tree automata have remained in chiefly theoretical spheres, there are no established testbeds from the "real world" against which to quantify the efficiency (or lack thereof) of new algorithms. Failing that, there is a need to generate suitable testbeds at random. Regrettably, there is little material in the literature regarding random generation of tree automata, and none at all regarding extensions such as Tree Automata with Global Equality and Disequality Constraints (TAGEDs). It should also be noted that what little material there is does not concern itself with the interest of the generated automata wrt. specific decision problems. In this report we present a scheme for random generation of positive TAGEDs, with a focus on making them interesting wrt. the Emptiness problem

Modélisation et vérification des processus métier orientés données probabilistes

There is a wide range of new applications that stress the need for business process models that are able to handle imprecise data. This thesis studies the underlying modelling and analysis issues. It uses as formal model to describe process behaviours a labelled transitions system in which transitions are guarded by conditions defined over a probabilistic database. To tackle verification problems, we decompose this model to a set of traditional automata associated with probabilities named as world-partition automata. Next, this thesis presents an approach for testing probabilistic simulation preorder in this context. A complexity analysis reveals that the problem is in 2-exptime, and is exptime-hard, w.r.t. expression complexity while it matches probabilistic query evaluation w.r.t. data-complexity. Then P-LTL and P-CTL model checking methods are studied to verify this model. In this context, the complexity of P-LTL and P-CTL model checking is in exptime. Finally a prototype called ”PRODUS” which is a modeling and verification tool is introduced and we model a realistic scenario in the domain of GIS (graphical information system) by using our approach.Un large éventail de nouvelles applications met l’accent sur la nécessité de disposer de modèles de processus métier capables de manipuler des données imprécises ou incertaines. Du fait de la présence de données probabilistes, les comportements externes de tels processus métier sont non markoviens. Peu de travaux dans la littérature se sont intéressés à la vérification de tels systèmes. Ce travail de thèse étudie les questions de modélisation et d’analyse de ce type de processus métier. Il utilise comme modèle formel pour décrire les comportements des processus métier un système de transitions étiquetées dans lequel les transitions sont gardées par des conditions définies sur une base de données probabiliste. Il propose ensuite une approche de décomposition de ces processus qui permet de tester la relation de simulation entre processus dans ce contexte. Une analyse de complexité révèle que le problème de test de simulation est dans 2-EXPTIME, et qu’il est EXPTIME-difficile en termes de complexité d’expression, alors que du point de vue de la complexité en termes des données, il n’engendre pas de surcoût supplémentaire par rapport au coût de l’évaluation de requêtes booléennes sur des bases de données probabilistes. L’approche proposée est ensuite étendue pour permettre la vérification de propriétés exprimées dans les logiques P-LTL et P-CTL. Finalement, un prototype, nommé ‘PRODUS’, a été implémenté et utilisé dans le cadre d’une application liée aux systèmes d’information géographiques pour montrer la faisabilité de l’approche proposée

Random Generation of Deterministic Tree (Walking) Automata

The original publication is a available at www.springerlink.comInternational audienceUniform random generators deliver a simple empirical means to estimate the average complexity of an algorithm. We present a general rejection algorithm that generates sequential letter-to-letter transducers up to isomorphism. We tailor this general scheme to randomly generate deterministic tree walking automata and deterministic top-down tree automata. We apply our implementation of the generator to the estimation of the average complexity of a deterministic tree walking automata to nondeterministic top-down tree automata construction we also implemented